>This is, surprise, going down a rathole fast, so this is my last pulic
>post on the topic...
>
>On Mon, 25 Mar 2002, Graham Klyne wrote:
>
>> At 10:05 AM 3/25/02 +0000, Jan Grant wrote:
>> >On Mon, 25 Mar 2002, Graham Klyne wrote:
>> >
>> > > I would argue that the "meaning" of some RDF is not the
>>"conjunction of the
>> > > meaning of individual triples". Conjunction of "meaning" seems to be a
>> > > meaningless (er, ill-defined) idea. It is the _truth_ under some
>> > > interpretation that is a conjunction.
>> >
>> >Unfortunately, that bit of the conversation seems to be missing from
>> >Dan's quoted text.
>>
>> OK.
>>
>> >Dan's concern might be summarised as: "...but what if a URI _doesn't_ I
>> >any R?" :-)
>>
>> By which I assume you mean have a mapping I(URI) in IR ?
>>
>> I think the definition of an interpretation requires that such a mapping
>> exists (irrespective of whatever may be happen in the "real Web").
>
>As I said to Dan: the MT defines an interpretation like this; it tells
>you what a "standard intended interpretation" will look like.
>
>It _would_ be possible to rewrite the MT document to use partial
>interpretation functions, but all the theorems and definitions would
>just have extra clauses (and proofs become similarly unmanageable) - for
>very little (no) gain.
>
>A better bet (I think) is to just do something Herbrandish - that is,
>keep the current definition of "interpretation"; if you _do_ wind up
>with one of Dan's problematical graphs (that is, one with a URI-labelled
>node with no "meaning", ie, which doesn't denote anything*), you don't
>really hurt yourself by letting it denote some mathematical figment that
>doesn't collide with anything else.
>
>I'm still not convinced that this is really a problem; just trying to
>summarise what's giving danbri sleepless nights.
I agree with Jan. One needs to be careful about using phrases like
'the referent', since the MT only assigns referents *in an
interpretation*, not in the *actual world* or even the *actual web*,
whatever that would mean. And there is always a satisfying
interpretation for any RDF graph, cf. the Herbrand lemma.
Dan's worry, I think, can be split into two parts. The 'social'
version is that people will in fact have some intended
interpretations in mind when they read RDF, and will be thinking
thoughts that are in some sense more concrete than the very broad set
of mathematical possibilities represented by 'all interpretations'.
(Answer: probably true, but irrelevant to questions of entailment and
to most pieces of software.) The 'technical' version is that we might
want to actually *say* that a given uriref fails to denote in some
interpretation, as a way of saying for example that it generates a
404 error, or something. Here I would agree with Jan: we *could* go
that way (RDF as a free logic) but the resulting technical complexity
would be a large cost and would not in fact buy us anything useful.
Right now the MT, if read strictly, does answer this question: any
asserted triple containing a name which does not refer in a given
interpretation is false in that interpretation, so the poison-URI
cases would presumably be those in which the graph asserts something
that is false in all the intended 'standard' interpretations, which
is another way of saying that it only has nonstandard satisfying
interpretations (eg those in which urirefs refer to themselves, like
literals). Similar things happen in most formal languages, which is
why there is a theory of nonstandard arithmetic.
Pat
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